MFV Reductions of MSSM Parameter Space

The 100+ free parameters of the minimal supersymmetric standard model (MSSM) make it computationally difficult to compare systematically with data, motivating the study of specific parameter reductions such as the cMSSM and pMSSM. Here we instead study the reductions of parameter space implied by using minimal flavour violation (MFV) to organise the R-parity conserving MSSM, with a view towards systematically building in constraints on flavour-violating physics. Within this framework the space of parameters is reduced by expanding soft supersymmetry-breaking terms in powers of the Cabibbo angle, leading to a 24-, 30- or 42-parameter framework (which we call MSSM-24, MSSM-30, and MSSM-42 respectively), depending on the order kept in the expansion. We provide a Bayesian global fit to data of the MSSM-30 parameter set to show that this is manageable with current tools. We compare the MFV reductions to the 19-parameter pMSSM choice and show that the pMSSM is not contained as a subset. The MSSM-30 analysis favours a relatively lighter TeV-scale pseudoscalar Higgs boson and $\tan \beta \sim 10$ with multi-TeV sparticles.Comment: 2nd version, minor comments and references added, accepted for publication in JHE

Challenges of Profile Likelihood Evaluation in Multi-Dimensional SUSY Scans

Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MultiNest, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MultiNest configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MultiNest is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.Comment: 21 pages, 9 figures, 1 table; minor changes following referee report. Matches version accepted by JHE

On NS5-brane instantons and volume stabilization

We study general aspects of NS5-brane instantons in relation to the stabilization of the volume modulus in Calabi-Yau compactifications of type II strings with fluxes, and their orientifold versions. These instantons correct the Kahler potential and generically yield significant contributions to the scalar potential at intermediate values of string coupling constant and volume. Under suitable conditions they yield uplifting terms that allow for meta--stable de Sitter vacua.Comment: 29 pages, 3 figures; statements about fields G^a made more precise, added some clarifications, typos correcte

Fitting the Phenomenological MSSM

We perform a global Bayesian fit of the phenomenological minimal supersymmetric standard model (pMSSM) to current indirect collider and dark matter data. The pMSSM contains the most relevant 25 weak-scale MSSM parameters, which are simultaneously fit using `nested sampling' Monte Carlo techniques in more than 15 years of CPU time. We calculate the Bayesian evidence for the pMSSM and constrain its parameters and observables in the context of two widely different, but reasonable, priors to determine which inferences are robust. We make inferences about sparticle masses, the sign of the $\mu$ parameter, the amount of fine tuning, dark matter properties and the prospects for direct dark matter detection without assuming a restrictive high-scale supersymmetry breaking model. We find the inferred lightest CP-even Higgs boson mass as an example of an approximately prior independent observable. This analysis constitutes the first statistically convergent pMSSM global fit to all current data.Comment: Added references, paragraph on fine-tunin

The impact of the ATLAS zero-lepton, jets and missing momentum search on a CMSSM fit

Recent ATLAS data significantly extend the exclusion limits for supersymmetric particles. We examine the impact of such data on global fits of the constrained minimal supersymmetric standard model (CMSSM) to indirect and cosmological data. We calculate the likelihood map of the ATLAS search, taking into account systematic errors on the signal and on the background. We validate our calculation against the ATLAS determinaton of 95% confidence level exclusion contours. A previous CMSSM global fit is then re-weighted by the likelihood map, which takes a bite at the high probability density region of the global fit, pushing scalar and gaugino masses up.Comment: 16 pages, 7 figures. v2 has bigger figures and fixed typos. v3 has clarified explanation of our handling of signal systematic

Tuning supersymmetric models at the LHC: A comparative analysis at two-loop level

We provide a comparative study of the fine tuning amount (Delta) at the two-loop leading log level in supersymmetric models commonly used in SUSY searches at the LHC. These are the constrained MSSM (CMSSM), non-universal Higgs masses models (NUHM1, NUHM2), non-universal gaugino masses model (NUGM) and GUT related gaugino masses models (NUGMd). Two definitions of the fine tuning are used, the first (Delta_{max}) measures maximal fine-tuning wrt individual parameters while the second (Delta_q) adds their contribution in "quadrature". As a direct result of two theoretical constraints (the EW minimum conditions), fine tuning (Delta_q) emerges as a suppressing factor (effective prior) of the averaged likelihood (under the priors), under the integral of the global probability of measuring the data (Bayesian evidence p(D)). For each model, there is little difference between Delta_q, Delta_{max} in the region allowed by the data, with similar behaviour as functions of the Higgs, gluino, stop mass or SUSY scale (m_{susy}=(m_{\tilde t_1} m_{\tilde t_2})^{1/2}) or dark matter and g-2 constraints. The analysis has the advantage that by replacing any of these mass scales or constraints by their latest bounds one easily infers for each model the value of Delta_q, Delta_{max} or vice versa. For all models, minimal fine tuning is achieved for M_{higgs} near 115 GeV with a Delta_q\approx Delta_{max}\approx 10 to 100 depending on the model, and in the CMSSM this is actually a global minimum. Due to a strong ($\approx$ exponential) dependence of Delta on M_{higgs}, for a Higgs mass near 125 GeV, the above values of Delta_q\approx Delta_{max} increase to between 500 and 1000. Possible corrections to these values are briefly discussed.Comment: 23 pages, 46 figures; references added; some clarifications (section 2

Direct Constraints on Minimal Supersymmetry from Fermi-LAT Observations of the Dwarf Galaxy Segue 1

The dwarf galaxy Segue 1 is one of the most promising targets for the indirect detection of dark matter. Here we examine what constraints 9 months of Fermi-LAT gamma-ray observations of Segue 1 place upon the Constrained Minimal Supersymmetric Standard Model (CMSSM), with the lightest neutralino as the dark matter particle. We use nested sampling to explore the CMSSM parameter space, simultaneously fitting other relevant constraints from accelerator bounds, the relic density, electroweak precision observables, the anomalous magnetic moment of the muon and B-physics. We include spectral and spatial fits to the Fermi observations, a full treatment of the instrumental response and its related uncertainty, and detailed background models. We also perform an extrapolation to 5 years of observations, assuming no signal is observed from Segue 1 in that time. Results marginally disfavour models with low neutralino masses and high annihilation cross-sections. Virtually all of these models are however already disfavoured by existing experimental or relic density constraints.Comment: 22 pages, 5 figures; added extra scans with extreme halo parameters, expanded introduction and discussion in response to referee's comment

Metastable SUSY Breaking, de Sitter Moduli Stabilisation and K\"ahler Moduli Inflation

We study the influence of anomalous U(1) symmetries and their associated D-terms on the vacuum structure of global field theories once they are coupled to N=1 supergravity and in the context of string compactifications with moduli stabilisation. In particular, we focus on a IIB string motivated construction of the ISS scenario and examine the influence of one additional U(1) symmetry on the vacuum structure. We point out that in the simplest one-Kahler modulus compactification, the original ISS vacuum gets generically destabilised by a runaway behaviour of the potential in the modulus direction. In more general compactifications with several Kahler moduli, we find a novel realisation of the LARGE volume scenario with D-term uplifting to de Sitter space and both D-term and F-term supersymmetry breaking. The structure of soft supersymmetry breaking terms is determined in the preferred scenario where the standard model cycle is not stabilised non-perturbatively and found to be flavour universal. Our scenario also provides a purely supersymmetric realisation of Kahler moduli (blow-up and fibre) inflation, with similar observational properties as the original proposals but without the need to include an extra (non-SUSY) uplifting term.Comment: 38 pages, 8 figures. v2: references added, minor correction

NLL soft and Coulomb resummation for squark and gluino production at the LHC

We present predictions of the total cross sections for pair production of squarks and gluinos at the LHC, including the stop-antistop production process. Our calculation supplements full fixed-order NLO predictions with resummation of threshold logarithms and Coulomb singularities at next-to-leading logarithmic (NLL) accuracy, including bound-state effects. The numerical effect of higher-order Coulomb terms can be as big or larger than that of soft-gluon corrections. For a selection of benchmark points accessible with data from the 2010-2012 LHC runs, resummation leads to an enhancement of the total inclusive squark and gluino production cross section in the 15-30 % range. For individual production processes of gluinos, the corrections can be much larger. The theoretical uncertainty in the prediction of the hard-scattering cross sections is typically reduced to the 10 % level.Comment: 45 pages, 16 Figures, LaTex. v2: published version. Grids with numerical results for the NLL cross sections for squark and gluino production at the 7/8 TeV LHC are included in the submission and are also available at http://omnibus.uni-freiburg.de/~cs1010/susy.htm

Accidental Inflation in the Landscape

We study some aspects of fine tuning in inflationary scenarios within string theory flux compactifications and, in particular, in models of accidental inflation. We investigate the possibility that the apparent fine-tuning of the low energy parameters of the theory needed to have inflation can be generically obtained by scanning the values of the fluxes over the landscape. Furthermore, we find that the existence of a landscape of eternal inflation in this model provides us with a natural theory of initial conditions for the inflationary period in our vacuum. We demonstrate how these two effects work in a small corner of the landscape associated with the complex structure of the Calabi-Yau manifold P^4_[1,1,1,6,9] by numerically investigating the flux vacua of a reduced moduli space. This allows us to obtain the distribution of observable parameters for inflation in this mini-landscape directly from the fluxes.Comment: 40 pages, 11 figure